Find the center of mass of the triangular region cut from the first quadrant by the line x + y = 3.

Question 1

Question 2

Denote the region by D. Its area is area(D) = 3·3/2 = 9/2 .

Next we calculate the integral

Because the region D *** unchanged when we swap x and y coordinates, the other integral has the same value,

Therefore the center of mass has the coordinates x¯=1 and ¯y = 1 .

kratos · Answer 1 · 2020-08-15T02:17:44+0000

Denote the region by D. Its area is area(D) = 3·3/2 = 9/2 .

Next we calculate the integral

Because the region D *** unchanged when we swap x and y coordinates, the other integral has the same value,

Therefore the center of mass has the coordinates x¯=1 and ¯y = 1 .

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